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Computers graphics based on linear algebra can't do true vanishing points, so... no? This isn't a tutorial on how to implement a useful three point perspective

Computers graphics based on linear algebra can't do true vanishing points, so... no? This isn't a tutorial on how to implement a useful three point perspective, this is an analysis of how three point perspective behaves if we don't make any computing concessions and examine the full space. You're never going to use that in 3D graphics, it looks terrible and I can't even think of a fun game mechanic that could be based on it. Just use a wide FOV camera in your software of choice and you'll get something much better. But it is a programming exercise that is worth running through. Remember, when we draw perspective on paper, we never draw all the way up to the vanishing points, we keep them far away enough that every straight line we draw still behaves like a straight line. Things don't get crazy until you get close enough to the vanishing points for the exponential mapping to become really pronounced, and starts doing really wild things. So obviously for an analysis of the space I'm going to draw something that is intentionally close enough to the vanishing points to show that insanity off =)

anderskaseorg 5y ago
Of course computer graphics based on linear algebra can do true vanishing points. It wouldn’t look right at all if it couldn’t. Perhaps what you’re missing is that 3D computer graphics actually uses 4D matrices with homogeneous coordinates. The extra dimension allows perspective projections to be represented, and also allows us to assign coordinates to vanishing points (points at infinity). The usual finite points are represented by (x, y, z, 1), and the vanishing point of (say) lines parallel to the x axis is represented by (1, 0, 0, 0). https://en.wikipedia.org/wiki/Homogeneous_coordinates#Use_in_computer_graphics_and_computer_vision https://en.wikipedia.org/wiki/Homogeneous_coordinates#Use_in...
robbrown451 5y ago
I don't know what your first sentence means. What are "true" vanishing points? What does it mean for computer graphics to "do" them? Basic computer graphics (linear algebra etc) does indeed create images that adhere to the rules of perspective. Lines that are parallel in 3d space, when projected onto the drawing plane, will now all intersect at a point on the plane. Etc. Whether or not the program actually calculates where that point is (typically, it doesn't) is not relevant. So what do you even mean by this? Have you defined vanishing points in some oddly obscure way that by definition can't be "done" by computer graphics? Maybe if you started your article with explaining how 3 point perspective is simply based on pinhole camera geometry (which is closely approximated by most camera lenses), it would help convince us that you are not simply stating a bunch of nonsense. I'm sorry but I don't know what else to say. The article doesn't seem to understand the basic theory of how perspective works, or has some odd idea of what it is that doesn't align with how others think about it. If somehow this aided understanding or insight, great, but it doesn't. Instead it simply tells people "don't bother understanding this thing, it is too complicated", but for no good reason. The article would do well to at least discuss this basic theory before delving into... weirdness. https://en.wikipedia.org/wiki/Pinhole_camera_model https://en.wikipedia.org/wiki/Pinhole_camera_model

anderskaseorg 5y ago

Of course computer graphics based on linear algebra can do true vanishing points. It wouldn’t look right at all if it couldn’t. Perhaps what you’re missing is that 3D computer graphics actually uses 4D matrices with homogeneous coordinates. The extra dimension allows perspective projections to be represented, and also allows us to assign coordinates to vanishing points (points at infinity). The usual finite points are represented by (x, y, z, 1), and the vanishing point of (say) lines parallel to the x axis is represented by (1, 0, 0, 0). https://en.wikipedia.org/wiki/Homogeneous_coordinates#Use_in_computer_graphics_and_computer_vision https://en.wikipedia.org/wiki/Homogeneous_coordinates#Use_in...

robbrown451 5y ago

I don't know what your first sentence means. What are "true" vanishing points? What does it mean for computer graphics to "do" them? Basic computer graphics (linear algebra etc) does indeed create images that adhere to the rules of perspective. Lines that are parallel in 3d space, when projected onto the drawing plane, will now all intersect at a point on the plane. Etc. Whether or not the program actually calculates where that point is (typically, it doesn't) is not relevant. So what do you even mean by this? Have you defined vanishing points in some oddly obscure way that by definition can't be "done" by computer graphics? Maybe if you started your article with explaining how 3 point perspective is simply based on pinhole camera geometry (which is closely approximated by most camera lenses), it would help convince us that you are not simply stating a bunch of nonsense. I'm sorry but I don't know what else to say. The article doesn't seem to understand the basic theory of how perspective works, or has some odd idea of what it is that doesn't align with how others think about it. If somehow this aided understanding or insight, great, but it doesn't. Instead it simply tells people "don't bother understanding this thing, it is too complicated", but for no good reason. The article would do well to at least discuss this basic theory before delving into... weirdness. https://en.wikipedia.org/wiki/Pinhole_camera_model https://en.wikipedia.org/wiki/Pinhole_camera_model